Subgroups — C₅²×Dic₁₄₃ #28384686

Order 14300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×Dic₁₄₃	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅×C₁₁×C₁₃	C₂×C₅	1	6	yes	—
5	C₅²×Dic₁₃	—	11	1	no	maximal, Hall
6	C₅²×Dic₁₁	—	13	1	no	maximal, Hall
7	C₅×C₁₁×C₁₃	C₄×C₅	1	6	yes	complemented
8	C₂×C₅²×C₁₃	D₁₁	1	1	yes	characteristic
9	Dic₁₄₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅²×C₁₁	D₁₃	1	1	yes	characteristic
11	C₅²×C₁₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₃	C₂×C₅²	1	1	yes	characteristic
13	C₅²×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
14	C₅×Dic₁₃	—	11	6	no	—
15	C₅×Dic₁₁	—	13	6	no	—
16	C₁₁×C₁₃	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₃	C₅×D₁₁	1	6	yes	—
18	C₂×C₅×C₁₁	C₅×D₁₃	1	6	yes	—
19	C₄×C₅²	—	143	1	no	Hall
20	C₅×C₁₃	C₅×Dic₁₁	1	6	yes	complemented
21	C₅×C₁₁	C₅×Dic₁₃	1	6	yes	complemented
22	Dic₁₃	—	11	1	no	Hall
23	C₂×C₅²	D₁₄₃	1	1	yes	characteristic
24	Dic₁₁	—	13	1	no	Hall
25	C₂×C₁₃	C₅²×D₁₁	1	1	yes	characteristic
26	C₅²	Dic₁₄₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	C₅²×D₁₃	1	1	yes	characteristic
28	C₄×C₅	—	143	6	no	—
29	C₁₃	C₅²×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₁₁	C₅²×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	C₅×D₁₄₃	1	6	yes	—
32	C₅	C₅×Dic₁₄₃	1	6	yes	direct product factor
33	C₄	—	143	1	no	Sylow
34	C₂	C₅²×D₁₄₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₁₄₃
commutator, hypocenter	C₁₁×C₁₃	C₄×C₅²
Frattini	C₂	C₅²×D₁₄₃
Fitting, socle, prime radical	C₂×C₅²×C₁₁×C₁₃	C₂
cosocle	C₂×C₁₁×C₁₃	C₂×C₅²
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₂×C₅²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₅²×C₁₁×C₁₃	C₄	semidirect
3. C₅×Dic₁₄₃	C₅	direct (N × H)
7. C₅×C₁₁×C₁₃	C₄×C₅	semidirect
9. Dic₁₄₃	C₅²	direct (N × H)
11. C₅²×C₁₃	Dic₁₁	semidirect
13. C₅²×C₁₁	Dic₁₃	semidirect
16. C₁₁×C₁₃	C₄×C₅²	semidirect
20. C₅×C₁₃	C₅×Dic₁₁	semidirect
21. C₅×C₁₁	C₅×Dic₁₃	semidirect
26. C₅²	Dic₁₄₃	direct (N × H)
29. C₁₃	C₅²×Dic₁₁	semidirect
30. C₁₁	C₅²×Dic₁₃	semidirect
32. C₅	C₅×Dic₁₄₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅²×C₁₁×C₁₃	2
C₅×Dic₁₄₃	5
C₅²×Dic₁₃	11
C₅²×Dic₁₁	13

Subgroups — C52×Dic143 #28384686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×Dic₁₄₃ #28384686